Monte Carlo Simulation of Some Dynamical Aspects of Drop Formation

Lima, Adriene Ribeiro; Penna, T. J. P.; Oliveira, Paulo Murilo Castro de

doi:10.1142/s012918319700093x

Cited by 7 publications

(2 citation statements)

References 11 publications

(21 reference statements)

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“…Chaotic dripping was originally suggested by Rössler [2] and experimentally confirmed by Shaw and his collaborators [3]. Since then, many experimental and theoretical studies have established the dripping faucet as a sort of paradigm for chaotic systems [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Most previous studies have involved measuring the time interval T n between successive drips, because the dripping time is easily measured using a drop-counter apparatus [3,4,5,6,7,8,9,10].…”

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“…The time intervals are then plotted in pairs (T n , T n+1 ) for each n to give a return map. Because the return maps typically appear low dimensional (∼ one-dimensional), the behavior is often described by a simple dynamical model composed of a variable mass and a spring [3,7,11,12,13,14,15]. In this massspring model, a mass point, whose mass increases linearly with time at a given flow rate Q, oscillates with a fixed value of the spring constant k; and a part ∆m of the total mass m is removed when the spring extension exceeds a threshold, which describes the breakup of a drop.…”

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Picture of the low-dimensional structure in chaotic dripping faucets

et al. 2003

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Chaotic dynamics of the dripping faucet was investigated both experimentally and theoretically. We measured continuous change in drop position and velocity using a high-speed camera. Continuous trajectories of a low-dimensional chaotic attractor were reconstructed from these data, which was not previously obtained but predicted in our fluid dynamic simulation. From the simulation, we further obtained an approximate potential function with only two variables, the drop mass and its position of the center of mass. The potential landscape helps one to understand intuitively how the dripping dynamics can exhibit low-dimensional chaos.Comment: 8 pages, 3 figure

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Picture of the low-dimensional structure in chaotic dripping faucets

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References

Oliveira¹,

Oliveira²,

Stauffer³

1999

TEUBNER-TEXTE Zur Physik

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Fragmentation experiment and model for falling mercury drops

Oliveira

Leite

Chianca

et al. 2007

Physica A: Statistical Mechanics and its Applications

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The experiment consists of counting and measuring the size of the many fragments observed after the fall of a mercury drop on the floor. The size distribution follows a power-law for large enough fragments. We address the question of a possible crossover to a second, different power-law for small enough fragments. Two series of experiments were performed. The first uses a traditional film photographic camera, and the picture is later treated on a computer in order to count the fragments and classify them according to their sizes. The second uses a modern digital camera. The first approach has the advantage of a better resolution for small fragment sizes. The second, although with a poorer size resolution, is more reliable concerning the counting of all fragments up to its resolution limit. Both together clearly indicate the real existence of the quoted crossover.The model treats the system microscopically during the tiny time interval when the initial drop collides with the floor. The drop is modelled by a connected cluster of Ising spins pointing up (mercury) surrounded by Ising spins pointing down (air). The Ising coupling which tends to keep the spins segregated represents the surface tension. Initially the cluster carries an extra energy equally shared among all its spins, corresponding to the coherent kinetic energy due to the fall. Each spin which touches the floor loses its extra energy transformed into a thermal, incoherent energy represented by a temperature used then to follow the dynamics through Monte Carlo simulations. Whenever a small piece becomes disconnected from the big cluster, it is considered a fragment, and counted. The results also indicate the existence of the quoted crossover in the fragment-size distribution.

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Monte Carlo Simulation of Some Dynamical Aspects of Drop Formation

Cited by 7 publications

References 11 publications

Picture of the low-dimensional structure in chaotic dripping faucets

Picture of the low-dimensional structure in chaotic dripping faucets

References

Fragmentation experiment and model for falling mercury drops

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